NUMERICAL MODELING OF OPTIONS IN DIFFUSION (B, S) STOCK MARKETS
Baitelieva A. Shakenov I. Shakenov K. Narbayeva S.
25 March 2025al-Farabi Kazakh State National University
KazNU Bulletin. Mathematics, Mechanics, Computer Science Series
2025#125Issue 181 - 89 pp.
This article examines the calculation of the option price V (t, x), the stock price x(t), and the optimal stopping (execution) time τ; (≡ t) over both finite and infinite time horizons. It then delves into determining a fair value for American-style options, leveraging the optimal stopping time within the framework of diffusion processes in stock markets, represented by (B, S). Additionally, the article explores the pricing of European-style options, starting with the buyer’s perspective and then transitioning to the seller’s viewpoint. The problems are solved either analytically, when the optimal stopping time is pre-determined, or numerically using methods like the sweep method and finite element techniques.These methods are applied by reducing the problem to Stefan’s problem, where Y* (t, x) represents the rational option value, τT* indicates the rational execution time, and x* (t) corresponds to the rational stock price.
equity diffusion markets , numerical modeling , option prices , options of American and European types , Stefan’s problem , stock prices
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Faculty of Mathematics and Mechanics, al-Farabi Kazakh National University, Almaty, Kazakhstan
Faculty of the International Schools of Economics of the Kazakh-British Technical University, Almaty, Kazakhstan
Faculty of Information Tehcnology, Al-Farabi Kazakh National University, Almaty, Kazakhstan
Faculty of Mathematics and Mechanics
Faculty of the International Schools of Economics of the Kazakh-British Technical University
Faculty of Information Tehcnology
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